CS 102B Robot Design Thursday, 111104

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CS 102B Robot DesignThursday, 11/11/04

• Todays Class
• Return Project 3
• Questions on Proximity Lab, Project 4?
• RCX Arithmetic
• Overflow and roundoff
• Boxcar averaging

• Lab work
• Modify proximity sensor code from Overmars, Chap.
  9, p. 30, to compare 4th reading with average of
  last 3 sensor readings (see Ferrari, p. 220)
• Time to work on Project 4
• Reading
• Ferrari Chap. 12, pp. 214-220

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An arithmetic example related to the RCX

• Suppose we have built a robot with the following
  properties (similar to Ferrari, pp. 72-73)
• Motor is connected to wheel with 13 ratio (so
  wheel rotates at 1/3 the rate of motor),
• Rotation sensor attached to motor axle (16 ticks
  per axle turn)
• Wheel diameter is 42.5 mm (Lego, from Denmark, is
  metric)
• Goal Write a subprogram that will make the robot
  go forward a specified distance.
• How is the distance traveled by the wheel related
  to the sensor reading?
• Distance traveled ?? (Wheel circumference)
  ( wheel axle turns)

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Example Solution

• Introduce some letters to represent quantities we
  know
• G gear ratio from wheel to motor 3
• R sensor ticks per turn 16
• S sensor reading
• D Wheel diameter 42.5
• Quantities we want to know
• T Traveled distance
• C Wheel circumference
• W wheel axle turns
• Also useful
• M motor axle turns

• The formula we need then is
• T C W
• How do we compute C?
• How do we compute W?
• Useful observations
• M S / R
• W M / G
• C ? D
• Do the math to solve for S!

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The function GoFwd(int T)

• //D diameter of wheel, G 1/(gear ratio),
• //R rotation sensor resolution
• define D 82
• define G 3
• define R 16
• task main()
• SetSensorType (SENSOR_1, SENSOR_TYPE_ROTATION)
  
• GoFwd(300)
• Wait(400)
• GoFwd(500)

void GoFwd(int T) int S (G R T) / (3
D) ClearSensor (SENSOR_1) OnFwd
(OUT_AOUT_C) until (abs(SENSOR_1) gt S)
Off (OUT_AOUT_C)
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Doing arithmetic with the RCX

• RCX uses integers only
• Numeric range -32768 to 32767 (16 bits)
• Overflow Any numbers that fall outside this
  range will interpreted incorrectly by the RCX
• Roundoff Errors that occur because all stored
  numbers are integers no fractions.
• GoFwd() example How close to correct are the RCX
  computations?
• Compute exact value of S and compare with RCX
  answer

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Avoiding Overflow and Roundoff Error

• Avoiding Overflow
• Avoid computing AB when A and B both large
• 182 182 33,124
• Avoiding Roundoff Error
• Dont divide smaller A by larger B
• A / B 0 if A lt B
• When computing A B / C, do multiplication
  first
• A (B / C) multiplies B/C remainder (error lt C)
  by A
• (A B) / C has error lt C
• Exception Dont multiply A B if product causes
  overflow!
• Which is better (A B) / C, or (A / C) (B / C)

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New math topic Boxcar Averaging

• Example Proximity Sensing
• Use IR reflection
• Repeatedly take sensor readings
• Compare latest to previous
• Turn if difference great enough
• What if we want to repeatedly compare latest to
  average of last three sensor readings
• Called boxcar averaging or moving average

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Computing averages

• Basic average rule to average values V1 to Vn
• A (V1 V2 ... Vn) / n
• When looking for change in sensor readings (to
  detect proximity), may want to compare to average
  of several previous readings to get sense of
  ambient values

9
Moving (boxcar) averages
int ave, v1, v2, v3 v2 SENSOR_1 v3
SENSOR_1 while (true) v1 v2 v2 v3
v3 SENSOR_1 ave (v1v2v3) / 3 //
other instructions...

• A moving average is a continually updated average
  of the most recent values
• Trace code at right, from Ferrari, p. 220